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3 years ago

7

You have taken over an abandoned project of drilling a water well. You find the hole is 22 feet deep. After 3 hours of drilling,

the depth is 33.4 ft. What depth would you expect to reach after 15 hours?

1 answer:

kondaur [170]3 years ago

6 0

33.4-22= 11.4
11.4/3= 3.8
3.8 is one hour.
3.8*15
57 ft. for the 15 hours.
57+33.4= 90.4 ft.
The answer is 90.4 ft.

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Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers

lora16 [44]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

$\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}$

Where <em>P</em> is the number of eggs laid, <em>x</em> is the number of workers, and <em>y</em> is the daily operating budget (assuming in US dollars $).

A)

We want to find dy/dx.

So, let’s find our equation in terms of <em>x</em>. We can raise both sides to 10/7. Hence:

$\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}$

Simplify:

$\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y$

Divide both sides by<em> </em>the <em>x</em> term to acquire:

$\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}$

Take the derivative of both sides with respect to <em>x: </em>

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]$

Apply power rule. Note that P is simply a constant. Hence:

$\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})$

Simplify. Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

We want to evaluate the derivative when <em>x</em> is 30 and when <em>y</em> is $10,000.

First, we will need to find <em>P</em>. Our original equations tells us that:

$P=x^{0.3}y^{0.7}$

Hence, at <em>x</em> = 30 and at <em>y</em> = 10,000, <em>P </em>is:

$P=(30)^{0.3}(10000)^{0.7}$

Therefore, for our derivative, we will have:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)$

Use a calculator. So:

$\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143$

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0

3 years ago

Y is a differentiable function of x. Choose the alternative that is the derivative dy / dx.

murzikaleks [220]

Differentiating both sides of

$x^3-y^3=1$

with respect to <em>x</em> yields (using the chain rule)

$3x^2 - 3y^2 \dfrac{\mathrm dy}{\mathrm dx} = 0$

Solve for d<em>y</em>/d<em>x</em> :

$3x^2 - 3y^2 \dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ 3y^2\dfrac{\mathrm dy}{\mathrm dx} = 3x^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{3x^2}{3y^2} = \dfrac{x^2}{y^2}$

The answer is then D.

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3 years ago

Need help with this problem, it's got me stuck PLZ

faust18 [17]

24x^2 +25x - 47 53

----------------------- = -8x -3 - ---------------

ax-2 ax-2

add 53/ax-2 to each side

24x^2 +25x - 47+53

----------------------- = -8x -3

ax-2

24x^2 +25x +6

----------------------- = -8x -3

ax-2

multiply each side by ax-2

24x^2 +25x +6 = (ax-2) (-8x-3)

multiply out the right hand side

24x^2 +25x +6 = -8ax^2 +16x-3ax +6

24 = -8a 25 = 16 -3a

a = -3 9 = -3a

a = -3

Choice B

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3 years ago

Determine if the expression -8c-9c^4d^2−8c−9c

Leto [7]

Answer:

$-8c-9c^4d^2-8c-9c$ is a polynomial of type binomial and has a degree 6.

Step-by-step explanation:

Given the polynomial expression

$-8c-9c^4d^2-8c-9c$

Group like terms

$=-9c^4d^2-8c-8c-9c$

Add similar elements: -8c-8c-9c=-25c

$=-9c^4d^2-25c$

Thus, the polynomial is in two variables and contains two, unlike terms. Therefore, it is a 'binomial' with two, unlike terms.

Each term has a degree equal to the sum of the exponents on the variables.

The degree of the polynomial is the greatest of those.

25c has a degree 1

$-9c^4d^2$ has a degree 6. (adding the exponents of two variables 'c' and 'd').

Thus,

$-8c-9c^4d^2-8c-9c$ is a polynomial of type binomial and has a degree 6.

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3 years ago

Which of the following number is the smallest 0.1,0.01,0.001,0.0001

atroni [7]

Answer:

0.0001

Step-by-step explanation:

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